14
14

Sep 21, 2013
09/13

by
Anatoliy K. Prykarpatsky

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14

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0

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0

A generalization of the classical Leray-Schauder fixed point theorem, based on the in finite- dimensional Borsuk-Ulam type antipode construction, is proposed. Two completely different proofs based on the projection operator approach and on a weak version of the well known Krein-Milman theorem are presented.

Source: http://arxiv.org/abs/0902.4416v1

9
9.0

Sep 21, 2013
09/13

by
Anatoliy K. Prykarpatsky

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9

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0

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0

A symplectic theory approach is devised for solving the problem of algebraic-analytical construction of integral submanifold imbeddings for integrable (via the nonabelian Liouville-Arnold theorem) Hamiltonian systems on canonically symplectic phase spaces.

Source: http://arxiv.org/abs/math/9905145v2

33
33

Jul 20, 2013
07/13

by
Anatoliy K. Prykarpatsky

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33

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0

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0

There is studied an invariant measure structure of a class of ergodicl discrete dynamical systems by means of the measure generating function method

Source: http://arxiv.org/abs/math/9906146v1

69
69

Jul 19, 2013
07/13

by
Ziemowit Popowicz; Anatoliy K. Prykarpatsky

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69

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0

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0

Based on the gradient-holonomic algorithm we analyze the integrability property of the generalized hydrodynamical Riemann type equation $%D_{t}^{N}u=0$ for arbitrary $N\in \mathbb{Z}_{+}.$ The infinite hierarchies of polynomial and non-polynomial conservation laws, both dispersive and dispersionless are constructed. Special attention is paid to the cases $%N=2,3$ and N=4 for which the conservation laws, Lax type representations and bi-Hamiltonian structures are analyzed in detail. We also show...

Source: http://arxiv.org/abs/1005.3942v1

10
10.0

Sep 21, 2013
09/13

by
Anatoliy K. Prykarpatsky; Denis Blackmore

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10

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0

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0

If we are given a smooth differential operator in the variable $x\in {\mathbb R}/2\pi {\mathbb Z},$ its normal form, as is well known, is the simplest form obtainable by means of the $\mbox{Diff}(S^1)$-group action on the space of all such operators. A versal deformation of this operator is a normal form for some parametric infinitesimal family including the operator. Our study is devoted to analysis of versal deformations of a Dirac type differential operator using the theory of induced...

Source: http://arxiv.org/abs/math/9907211v1

7
7.0

Sep 23, 2013
09/13

by
Nikolai N. Bogolubov, Jr.; Anatoliy K. Prykarpatsky

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7

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0

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0

The main fundamental principles characterizing the vacuum field structure are formulated and the modeling of the related vacuum medium and charged point particle dynamics by means of devised field theoretic tools are analyzed. The work is devoted to studying the vacuum structure, special relativity, electrodynamics of interacting charged point particles and quantum mechanics, and is a continuation of \cite{BPT,BRT1}. Based on the vacuum field theory no-geometry approach, the Lagrangian and...

Source: http://arxiv.org/abs/0810.3303v2

23
23

Jul 22, 2013
07/13

by
Anatoliy K. Prykarpatsky; Nikolai N. Bogolubov Jr

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23

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0

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0

The nature of space-time and surrounding matter objects was and persists to be a one of the most intriguing and challenging problems facing the mankind and natural scientists especially. As we know one of the most brilliant inventions in physics of XIX-th century was combining of electricity and magnetism within the Faraday-Maxwell electromagnetism theory. This theory explained the main physical laws of light propagation in space-time and posed new questions concerning the nature of vacuum....

Source: http://arxiv.org/abs/0807.3691v9

11
11

Sep 22, 2013
09/13

by
Yarema Prykarpatsky; Anatoliy Samoilenko; Anatoliy K. Prykarpatsky

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11

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0

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0

A differential geometrical and topological structure of Delsarte transmutation operators in multidimension is studied, the relationships with De Rham-Hodge-Skrypnik theory of generalized differential complexes is stated.

Source: http://arxiv.org/abs/math-ph/0403054v1

5
5.0

Sep 21, 2013
09/13

by
Anatoliy K. Prykarpatsky; Nikolai N. Bogoliubov Jr.; Jolanta Golenia

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5

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0

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0

Symplectic and symmetry analysis for studying MHD superfluid flows is devised, a new version of the Z. Peradzynski helicity theorem based on differential - geometric and group-theoretical methods is derived. Having reanalyzed the Peradzynski helicity theorem within the modern symplectic theory of differential- geometric structures on manifolds, a new unified proof and a new generalization of this theorem for the case of compressible MHD superfluid flow are proposed. As a by-product, a sequence...

Source: http://arxiv.org/abs/0902.4408v1

14
14

Sep 21, 2013
09/13

by
Nikolai N. Bogolubov Jr.; Denis Blackmore; Anatoliy K. Prykarpatsky

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14

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0

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0

We review the modern classical electrodynamics problems and present the related main fundamental principles characterizing the electrodynamical vacuum-field structure. We analyze the models of the vacuum field medium and charged point particle dynamics using the developed field theory concepts. There is also described a new approach to the classical Maxwell theory based on the derived and newly interpreted basic equations making use of the vacuum field theory approach. In particular, there are...

Source: http://arxiv.org/abs/1204.5129v4

31
31

Sep 23, 2013
09/13

by
Yarema A. Prykarpatsky; Denis Blackmore; Jolanta Golenia; Anatoliy K. Prykarpatsky

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31

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0

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0

An approach based on the spectral and Lie - algebraic techniques for constructing vertex operator representation for solutions to a Riemann type Gurevicz-Zybin hydrodynamical hierarchy is devised. A functional representation generating an infinite hirerachy of dispersive Lax type integrable flows is obtaned.

Source: http://arxiv.org/abs/1105.4403v3

7
7.0

Sep 22, 2013
09/13

by
Jolanta Golenia; Maxim V. Pavlov; Ziemowit Popowicz; Anatoliy K. Prykarpatsky

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7

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0

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0

Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm. The bi-Hamiltonicity and complete integrability of the corresponding dynamical system is stated and an infinite hierarchy of commuting to each other conservation laws of dispersive type are found. The well defined regularization of the model is constructed and its Lax type integrability...

Source: http://arxiv.org/abs/1001.1145v2

12
12

Sep 21, 2013
09/13

by
Anatoliy K. Prykarpatsky; Nikolai N. Bogolubov; Jolanta Golenia; Ufuk Taneri

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12

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0

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0

Introductive backgrounds of a new mathematical physics discipline - Quantum Mathematics - are discussed and analyzed both from historical and analytical points of view. The magic properties of the second quantization method, invented by V. Fock in 1932, are demonstrated, and an impressive application to the nonlinear dynamical systems theory is considered.

Source: http://arxiv.org/abs/0902.4411v1

23
23

Sep 21, 2013
09/13

by
Nikolai N. Bogolubov Jr.; Anatoliy K. Prykarpatsky; Ufuk Taneri

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23

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0

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0

The main fundamental principles characterizing the vacuum field structure are formulated, the modeling of the related vacuum medium and charged point particle dynamics by means of devised field theoretic tools are analyzed. The Maxwell electrodynamic theory is revisited and newly derived from the suggested vacuum field structure principles, the classical special relativity theory relationship between the energy and the corresponding point particle mass is revisited and newly obtained. The...

Source: http://arxiv.org/abs/0808.0871v7

7
7.0

Sep 22, 2013
09/13

by
Denis Blackmore; Jolanta Golenia; Yarema A. Prykarpatsky; Anatoliy K. Prykarpatsky

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7

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0

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0

Invariant ergodic measures for generalized Boole type transformations are studied using an invariant quasi-measure generating function approach based on special solutions to the Frobenius--Perron operator. New two-dimensional Boole type transformations are introduced, and their invariant measures and ergodicity properties are analyzed.

Source: http://arxiv.org/abs/1210.1746v3

5
5.0

Sep 19, 2013
09/13

by
Yarema A. Prykarpatsky; Nikolai N. Bogolubov Jr; Anatoliy K. Prykarpatsky; Valeriy H. Samoylenko

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5

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0

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0

A gradient-holonomic approach for the Lax type integrability analysis of differentialdiscrete dynamical systems is devised. The asymptotical solutions to the related Lax equation are studied, the related gradient identity is stated. The integrability of a discrete nonlinear Schredinger type dynamical system is treated in detail.

Source: http://arxiv.org/abs/1010.2531v2

6
6.0

Sep 21, 2013
09/13

by
Denis Blackmore; Yarema A. Prykarpatsky; Orest D. Artemowych; Anatoliy K. Prykarpatsky

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6

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0

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0

The complete integrability of a generalized Riemann type hydrodynamic system is studied by means of symplectic and differential-algebraic tools. A compatible pair of polynomial Poissonian structures, Lax type representation and related infinite hierarchy of conservation laws are constructed.

Source: http://arxiv.org/abs/1204.0251v4

98
98

Jul 19, 2013
07/13

by
Bohdan Yu. Kyshakevych; Anatoliy K. Prykarpatsky; Denis Blackmore; Ivan P. Tverdokhlib

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98

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0

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0

A competing market model with a polyvariant profit function that assumes "zeitnot" stock behavior of clients is formulated within the banking portfolio medium and then analyzed from the perspective of devising optimal strategies. An associated Markov process method for finding an optimal choice strategy for monovariant and bivariant profit functions is developed. Under certain conditions on the bank "promotional" parameter with respect to the "fee" for a missed...

Source: http://arxiv.org/abs/1005.2661v1

19
19

Sep 21, 2013
09/13

by
Yarema A. Prykarpatsky; Orest D. Artemovych; Maxim V. Pavlov; Anatoliy K. Prykarpatsky

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19

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0

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0

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic hierarchy is revisited, its new Lax type representation and Poisson structures constructed in exact form. The related bi-Hamiltonian integrability and compatible Poissonian structures of the generalized Riemann type hierarchy are also discussed.

Source: http://arxiv.org/abs/1108.0878v6

29
29

Jul 19, 2013
07/13

by
Anatoliy K. Prykarpatsky; Orest D. Artemovych; Ziemowit Popowicz; Maxim V. Pavlov

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29

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0

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0

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic equations at N = 3; 4 is devised. The approach is also applied to studying the Lax type integrability of the well known Korteweg-de Vries dynamical system.

Source: http://arxiv.org/abs/1005.2660v4